On a class of nonlinear two-level operator-difference schemes with weights (Q1909829)

The author studies the well-posedness of two-level schemes for time dependent problems. The spatial finite difference operator is presented as a decomposition of two operators with appropriate properties. Such representation leads to a unified approach for studying the stability of the schemes for a wide class of nonlinear parabolic and hyperbolic equations. The theory is illustrated on the one-dimensional system of equations of gas dynamics written in Lagrangian mass coordinates.